Genesis 1 tells the creation story in terms of who and why not how and when.Like many cliches it sounds pithy but on closer inspection lacks substance. The statement is analysing the first chapter of the Bible from the viewpoint of who, why, how and when. It is useful to read the chapter with these questions in mind.
The repeated use of the word God thru out the chapter certainly supports the observation that Genesis 1 tells us who created.
What about the "why"? I can see very little in the first chapter that tells us why God created the universe. That he did, yes; but his motivation for doing so, no. We are informed that the stellar objects are for light and time keeping and the vegetation is for food; so there is a "why" for creation in terms of man's relationship with them, but the reason for making man? In fact it is difficult to find much in the Bible that tells us why God created us. A explanation would be that he is love and created creatures, including man, to offer love as a gift. While that is likely true, it is an indirect teaching of Scripture and is not obvious in Genesis 1.
Does Genesis 1 tell us how God created? Only in a limited form. That all started from the deep (water) and hence possibly some creations were made from water; that space was created by separating the waters; in terms of land and seas being gathered together which may have some implications for geology. Genesis 2 gives information on the "how" of man. Male was made from dust and God's breath, which may have some theological implications but less certain scientific ones; and female from male, again for theological reasons: in order to teach us about marriage. While some "how" information may be garnered from the chapter, it is not a primary teaching.
Which leaves the "when". The term "when" in the phrase above is used to mean that Genesis 1 does not give us chronological information. So strictly the "when" is not given in the first chapter, it is from later chapters in Genesis and elsewhere in Scripture. But that Genesis 1 gives chronological information is certain. The chapter repeatedly uses statements that give a chronological flow.
Therefore if someone subscribes to a hermeneutic that doesn't agree with Genesis 1 describing 6 literal days, it is unreasonable to disparage those who think it does.
So the quote may be better rephrased:
Genesis 1 tells the creation story in terms of who and when but gives little information on how and why.